Decentralized Control of Traffic Networks

Abstract

In this chapter, novel centralized and decentralized routing control strategies based on minimization of the worst-case queuing length are proposed. The centralized routing problem is formulated as an \(\mathcal{H}_{\infty}\) optimal control problem to achieve a robust routing performance in presence of multiple and unknown fast time-varying network delays. Unlike similar previous work in the literature the delays in the queuing model are assumed to be unknown and time-varying. A Linear Matrix Inequality (LMI) constraint is obtained to design a delay-dependent \(\mathcal{H}_{\infty}\) controller. The physical constraints that are present in the network are then expressed as LMI feasibility conditions. Our proposed centralized routing scheme is then reformulated in a decentralized frame work. This modification yields an algorithm that obtains the “fastest route”, increases the robustness against multiple unknown time-varying delays, and enhances the scalability of the algorithm to large scale traffic networks. Simulation results are presented to illustrate and demonstrate the effectiveness and capabilities of our proposed novel dynamic routing strategies.